MATHEMATICS HIGH SCHOOL

The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest hundredth. A. 6.69 inches
B. 6.25 inches
C. 7 inches
D. 13.38 inches

Answers

Answer 1
Answer: The circumference of the wheel can be expressed by:

circumference = 2 \pi r
Where r = the radius of the wheel.

Since the spoke reaches from the center of the wheel to its rim then r = length of the spoke

By rearranging the circumference equation we get:

r = (circumference)/(2 \pi )

If circumference = 42 inches then:

r = (42)/(2 \pi )

r = 6.68
Which is closest to B

Your book may have a typo in it as the answer to 4 decimal places is 6.6845 which rounds down to 6.68, not up to 6.69.

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Carole earns $2.50 for each gadget she completes. What was her gross pay if she completed 145 gadgetslast week?

Answers

2.50 per gadget multiplied by 145 gadgets is a total of 362.50.

A right triangle has a hypotenuse of length 59 and one leg of length 23. Part A: Determjne the angle measure of the other two acute angles in the triangle. Round to the nearest hundredth.

Part B: Determine the side length of the other leg.

Answers

Answer:

Part A) The measure of the other two acutes angles are =67.06\° and 22.94\°  

Part B) The side length of the other leg is equal to 54.33\ units

Step-by-step explanation:

Part A)

see the attached figure to better understand the problem

we know that

In the right triangle ABC

cos(A)=(AB)/(AC)

substitute the values

cos(A)=(23)/(59)

A=arccos((23)/(59))=67.06\°

Remember that

A+C=90\° -------> by complementary angles

C=90\°-67.06\°=22.94\°    

Part B)

Applying the Pythagoras Theorem

CB^(2)=AC^(2)-AB^(2)

substitute

CB^(2)=59^(2)-23^(2)

CB^(2)=2,952

CB=54.33\ units

The function g(x) = –3x2 – 36x – 60 written in vertex form is g(x) = –3(x + 6)2 + 48. Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60? The graph of f(x) = x2 is made narrower. The graph of f(x) = x2 is shifted right 6 units. The graph of f(x) = x2 is shifted down 48 units. The graph of f(x) = x2 is reflected over the y-axis.

Answers

The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
and a indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.

Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis
The graph is made narrower.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.

From the choices we only have:
The graph of f(x) = x2 is made narrower

A. The graph of f(x) = x2 is made narrower.

I took the test and that was the answer i got.

Jude has seven times as many dimes as nickels their value is $5.25 how many nickels does he have.49
15
7

Answers

Let dimes be represented by d and n for nickels;
1 dime= 0.1 dollars
1 nickel=0.05 dollars
0.1d+0.05n=5.25
d=7n
so,
0.1(7n)+0.05n=5.25
0.7n+0.05n=5.25
0.75n=5.25
n=7
There are 7 nickels and 49 dimes
1 nickel = $0.05
1 dime = $0.10

n - number of nickels
7n - number of dimes

A equation:
 
0.05n + 0.1 · 7n = 5.25
0.05n + 0.7n = 5.25
0.75n = 5.25          |divide both sides by 0.75
n = 7

Answer: He have 7 nickels.

How do you find the circumference when you ONLY know the area?

Answers


It's easy if you remember the formulas you learned for the area, diameter,
and circumference of a circle:

-- Area = (pi) (radius)²
-- Diameter = (2) (radius)
-- Circumference = (pi) (diameter)

You know the area. So let's use the first formula to find the circle's radius.

Area = (pi) (radius)²

Divide each side by (pi):      Area/pi  =  (radius)²

                                            Radius = √(area/pi)

Now use the second formula to find the circle's diameter:

Diameter = (2) (radius)

Diameter = 2 √(area/pi)

Now use the third formula to find the circle's circumference:

Circumference = (pi) (diameter)

Circumference = (pi) (2) √(area/pi)

With just a little tweak, that can be written slightly more simply:

Circumference = 2 √(pi x area)

See ?  Just the three circle formulas,and a lot of massaging.

Solve if you are a genius.No trick. Pure math. Gud luck Solve it

You are standing in one big palace where a king and his 5 queens stay.
Each queen has 5 rooms. In each room there are 5 big cats.
Each big cat has 5 little cats. Each cat has 4 legs.How many legs are there in the palace?

Take ur time...Solve if you are a genius.

No trick. Pure math. Gud luck Solve it

You are standing in one big palace where a king and his 5 queens stay.
Each queen has 5 rooms. In each room there are 5 big cats.
Each big cat has 5 little cats. Each cat has 4 legs.How many legs are there in the palace?

Take ur time...

Answers

ok, we don't know if anyone is in there, maybe they all went grocery shopping
in that scenario, you are the only one (I hope) and therefor answer is 2 legs

if everybody is in ther (including yourself)

king=1
queens=5
how many rooms total?
5 times 5=25 rooms
5 big cats per room
5 times 25=125 big cats
each big cat has 5 little cats
125 times 5=625 little cats


1 king
5 queens
125 big cats
625 little cats

people has 2 legs
casts have 4
1*2+5*2+125*4+625*4=3012 legs
plus yourself (2 legs)
3014 legs






2 answers
1. you are alone in pallace, quesiton never mentioned that the king and co were in the pallace, only yourself, therfor answer is 2 legs (yours)
2. everybody is in there including yourself, and answer is 3014 legs
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